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Numerical analysis of anion-exchange membranedirect glycerol fuel cells under steady state anddynamic operations

Xiaotong Han 1,2, David J. Chadderdon 1,2, Ji Qi 1, Le Xin, Wenzhen Li*,1,Wen Zhou**

Department of Chemical Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton,

MI 49931, USA

a r t i c l e i n f o

Article history:

Received 3 June 2014

Received in revised form

26 August 2014

Accepted 28 August 2014

Available online 13 October 2014

Keywords:

Fuel cell

Dynamic simulation

Glycerol oxidation

Gold nanoparticles

Mass transport

* Corresponding author. Tel.: þ1 515 294 458** Corresponding author. Tel.: þ1 906 487 116

E-mail addresses: wzli@iastate.edu, liwen1 Current address: Department of Chemic2 Xiaotong Han and David J. Chadderdon

http://dx.doi.org/10.1016/j.ijhydene.2014.08.10360-3199/Copyright © 2014, Hydrogen Ener

a b s t r a c t

This work develops a one-dimensional model of an alkaline anion-exchange membrane

direct glycerol fuel cell (AEM-DGFC) for cogeneration of tartronate and electricity. The

model is validated against steady state and dynamic experiments, and shows good

agreement. Steady state modeling includes anode and cathode losses and predicts the

single cell polarization and power density curves. Coupled mass transport, charge trans-

port, and electrochemical kinetics predict the effects of varying reactant concentration and

diffusion layer porosity on single cell performance. The results show that anode over-

potential is the major source of loss at middle to high current density regions, due to

limited glycerol diffusion at the catalyst layer. Furthermore, the dynamic response of AEM-

DGFC to step changes in current density is simulated by considering time-dependent

species transport and double-layer capacitance charging. Analysis of dynamic simulation

reveals that the liquid-phase reactant diffusion is a key factor influencing the transient

AEM-DGFC behavior and is very sensitive to diffusion layer design. This new numerical

analysis of a glycerol-fed fuel cell demonstrates that a simple, single oxidation product

model can successfully predict the steady state and dynamic losses.

Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

Introduction

The increasingly urgent need for renewable sources of energy

and fine chemicals to replace petroleum has driven huge ef-

forts to develop sustainable and economically-feasible cata-

lytic processes for the refinement of natural materials [1e4].

2; fax: þ1 515 294 2689.4.zhen@gmail.com (W. Li)al and Biological Engineercontributed equally to thi44gy Publications, LLC. Publ

Being a polyol which is massively produced during biodiesel

manufacturing, glycerol is considered a key biorenewable

building-block for the production of many chemicals [5].

Among them, fine chemicals including glyceric acid (GA),

tartronic acid (TA) and mesoxalic acid (MA) are products of

glycerol oxidation reaction (GOR) [6]. Aqueous phase selective

, wzhou1@mtu.edu (W. Zhou).ing, Iowa State University, Ames, IA 50011, USA.s work.

ished by Elsevier Ltd. All rights reserved.

Fig. 1 e Schematic drawing of an AEM-DGFC and model

domains including diffusion layers (DL), catalyst layers

(CL), and anion-exchange membrane (AEM).

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 919768

oxidation of glycerol to valuable chemicals over metal cata-

lysts with O2, air, or H2O2 oxidants is a very attractive green

process due to its low environmental impact, and has been

exhaustively researched [5e20]. However, conventional het-

erogeneous catalytic oxidation of glycerol cannot take

advantage of the energy stored in the chemical bonds of

glycerol, which can be converted directly into electrical energy

through electrochemical oxidation in a fuel cell type reactor.

Low-temperature anion-exchange membrane fuel cells

(AEMFC) have attracted enormous attention, owing to fast

electrochemical kinetics, reduced fuel crossover, and a

friendly alkaline environment allowing use of non-platinum

catalyst [21]. Anion-exchange membrane direct glycerol fuel

cells (AEM-DGFCs) are of special interest for the prospect of

simultaneously producing electricity and valuable oxidation

products [22e28]. Significant works on AEM-DGFC have made

progress in improving electrical energy generation perfor-

mance, however output power density remains limited by low

selectivity to completely oxidized CO2 or other deeply oxidized

carboxylates [28]. Recently, Zhang et al. discovered that deep

oxidation of glycerol (to TA and MA) was greatly facilitated

with carbon-cloth based porous electrodes compared to

smooth electrodes [29]. Even more recently, remarkable

selectivity to TA (70.2% selectivity) was achieved on Au/C

(carbon-supported gold nanoparticle catalyst) in an AEM-

DGFC by tuning electrode structure and operating conditions

[30]. Although much progress has been made in catalyst and

reactor design through trail-and-error experiments for selec-

tive electrocatalytic oxidation, it remains a challenge to isolate

the individual effects of mass transport, charge transport, and

electrochemical kinetics on cell performance. However,

mathematical modeling is a powerful and economical tool

that, when combinedwith experimental results, may quantify

those complicated physicochemical processes [31].

Previously, extensive fuel cell modeling works have

focused on proton exchange membrane fuel cells (PEMFC)

[32e36], however more recent efforts have been spent devel-

oping mathematical models of hydrogen, alcohol, and

glucose-fed AEMFCs. An early one-dimensional, steady state

study applied Tafel expressions to model electrode reactions

and a multi-layer membrane model in order to study mass

transport in an alkaline direct ethanol fuel cell [37]. Multi-

dimensional, steady state and dynamic models were devel-

oped for the anode of H2/O2 AEMFC to study the effect of

operating conditions on the transient distribution of liquid

water in the anode [38,39]. An analytical model was recently

reported for an alkalinemembrane directmethanol fuel cell to

identify the most significant factors affecting cell perfor-

mance including methanol crossover and water transport

limitations [40]. A three-dimensional, non-isothermal model

of alkaline AEMFC was developed to study effects of anode

humidification, water removal mechanisms, and water

transport in the membrane [41]. Zhao's group recently pub-

lished an elegant work on direct ethanol AEMFCs using a

relatively simple one-dimensional model and assuming 100%

selectivity to a single ethanol oxidation product, acetic acid

[42]. This simplified approach was sufficient for investigating

the effects of operating and design parameters on electricity

generation performance. Similarly, a simple model of a direct

glucose AEMFC considering mass transport and a single-

product electrochemical oxidation reaction was developed,

and found that unlike with other fuels, the anodic over-

potential from glucose oxidation was quite large compared to

the cathodic or ohmic losses [43]. However, to the best of our

knowledge, suchmodels have not been applied to glycerol fuel

in AEMFC, partially as a result of the low selectivity to one

particular GOR product previously achieved in anion-

exchange membrane (AEM) reactors. Mathematical modeling

of AEM-DGFC may reveal the unique behavior of glycerol as

fuel, which hasmuch higher viscosity and a greater number of

electrons extracted from a single molecule (8.0 electrons for

GLY to TA, compared to 4.0 electrons for ethanol oxidation to

acetic acid) in oxidation compared to smaller alcohols such as

ethanol and methanol.

Herein, a study of performance and behavior of AEM-DGFC

with Au/C anode catalyst for cogeneration of electricity and

TA, the most valuable GOR product, is conducted in terms of

operating and structural design parameters. This work com-

bines theoretical modeling, which integrates mass transport,

charge transport, and electrochemical kinetics in steady state

and dynamic domains with experimental testing for param-

eter determination and model validation. Steady state

modeling predicts thermodynamic and kinetic losses under

stable operating conditions, while the dynamic model reveals

the dominant mechanisms of transient behavior under

changing load conditions. Original laboratory experiments are

performed to evaluate the steady state currentevoltage rela-

tionship and dynamic responses to step changes in current

density and AC current perturbations (EIS) in order to better

understand and model the complex physicochemical pro-

cesses of the AEM-DGFC.

Methods

Model formulation and assumptions

Fig. 1 shows the physical model domain including anode and

cathode porous diffusion layers (DL) and catalyst layers (CL),

separated by an anion-exchange membrane (AEM). GOR and

oxygen reduction reaction (ORR) occur at the anode and

cathode CLs, respectively, which are treated as interfaceswith

no physical thickness. Therefore, all mass transport resis-

tance is represented in the porousDLs. The bulk flow channels

Table 2 e Mass and charge transport parameters.

Parameter Symbol Value Units Reference

Diffusion

coefficient of GLY

DGLY 2.824 � 10�9 m2 s�1 [45]

�9 2 �1

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represent the boundary where fresh fuel is available at bulk

concentrations, but are outside the model domain, which is

bounded by points x0 and x3 in Fig. 1. Geometric dimensions

and physical parameters of the model domain are shown in

Table 1.

An important simplifying assumption is that GOR forms a

single product, TA. We hypothesize that a single electro-

chemical oxidation reaction model can effectively predict the

voltage losses and performance of an AEM-DGFC with Au/C

anode catalyst due to the high product selectively (70.6% TA)

recently achieved [30]. Theoretical standard cell potential is not

overly sensitive to varying product distribution in this case,

given that the standard cell potentials assuming GA, TA, or MA

oxidation products are similar (i.e. 1.14, 1.17, or 1.12 V, respec-

tively) [25]. Furthermore, the average number of electrons

transferred experimentally on Au/C anode catalyst was esti-

mated from reported product selectivity and ranged from 6.6 to

7.2 electrons per molecule GLY during a 12 h reaction (calcu-

lated from Ref. [30]), which is near the 8.0 electrons transferred

for a single molecule of TA product used in this model. We

propose that these values are sufficiently similar to predict the

relationship between GLY molar consumption and faradaic

current, which is critical for modeling species mass transport.

The proposed model will be verified by comparison to original

experimental tests under steady state and dynamic operations.

On the anode, GOR consumes GLY and hydroxideions (OH)

and generates TA, water, and electrons:

C3H8O3 þ 8OH�/C3H4O5 þ 6H2Oþ 8e� Ea0 ¼ �0:77 V vs: SHE

(1)

The generated TA is rapidly neutralized in alkaline solution

and consumes 2 mol OH per mole TA to form tartronate ion

(TAR):

C3H4O5 þ 2OH�/ðC3H2O5Þ2� þ 2H2O (2)

Product neutralization is a non-faradaic reaction and

therefore does not contribute to the theoretical standard cell

potential. On the cathode, oxygen reduction reaction (ORR) is

the electron accepting reaction and also the generating source

of OH:

2O2 þ 4H2Oþ 8e�/8OH� Ec0 ¼ 0:40 V vs: SHE (3)

The generated OH at the cathode is transported through

the AEM to the anode for GOR. The overall reaction including

GOR, ORR, and TA neutralization becomes:

C3H8O3 þ 2O2 þ 2OH�/ðC3H2O5Þ2� þ 4H2O E0 ¼ 1:17 V (4)

In order to accurately model the desired electrochemical

and physical phenomenon while maintaining reasonable

Table 1 e Geometric dimensions and physicalparameters.

Parameter Symbol Value Units Reference

Porosity of anode DL εADL 0.56 e Fitted

Porosity of cathode DL εCDL 0.73 e [42]

Thickness of anode DL lADL 3.0 � 10�4 m Measured

Thickness of cathode DL lCDL 1.6 � 10�4 m Measured

Thickness of membrane lm 1.0 � 10�5 m [44]

calculation times, additional simplifications and approxima-

tions are made: (1) fuel cell operates under isothermal condi-

tions, (2) reactant availability is predominately controlled by

diffusion, while convective transport from bulk fluid flow and

adsorption/desorption processes are neglected, (3) electro-

chemical reactions occur at the anode and cathode CLs, which

are treated as interfaces with no thickness, and (4) species

crossover through the membrane is ignored. Note that the Fe-

based cathode catalyst is not active for GOR, so mixed-

potentials from GLY crossover are not expected. Also, OH

generated at the cathode is immediately available for GOR at

the anode, however the resistance to ion transport is included

in the calculation of cell voltage.

Mass transportMass transport of reaction species is considered in the

through-plane direction (x-direction, Fig. 1) and is assumed to

be diffusion dominated and described by Fick's 2nd Law:

dCi

dt¼ Deff

i

d2Ci

dx2(5)

where Ci is concentration and Deffi is the effective diffusion

coefficient of species i. For the steady state modeling, con-

centration does not changewith time and the left-hand side of

Fick's Law is zero. A numerical solution is found after applying

physical and electrochemical boundary/initial conditions,

described in later sections. The effective diffusion coefficient

accounts for the porosity of anode or cathode DLs:

Deffi ¼ ε

3=2Di (6)

where Di is the species diffusion coefficient and ε is DL

porosity. Porosity is difficult to measure because the DLs are

under compression inside the fuel cell assembly and the

transport properties can be significantly different than when

uncompressed. Therefore, the anode DL porosity value is

instead estimated based on the observed limiting current

density in steady state experimental tests. Diffusion co-

efficients for GLY, OH, and TAR in water and O2 in air are

given at 333 K in Table 2. Little physical information is

available on TAR, so the diffusion rates are approximated as

equal to GLY, based on their similar molecular structure and

size.

Diffusion

coefficient of OH

DOH 5.260 � 10 m s [45]

Diffusion

coefficient of TAR

DTAR 2.824 � 10�9 m2 s�1 Assumed

Diffusion

coefficient of O2

DO2 2.742 � 10�5 m2 s�1 [45]

OH conductivity

of membrane

sm 3.8 (U m)�1 [44]

Contact resistance Rcontact 4.48 � 10�6 U m2 Measureda

a Total ohmic resistance measured by current-interrupt method

minus membrane resistance.

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Electrochemical kineticsThe relationship of the faradaic current density (j) with elec-

trode overpotential (h) is given by the ButlereVolmer equation

[46] and shown for GOR at the anode (a) and ORR at the

cathode (c):

ja ¼ �j0;a

�exp

�aaFRT

ha

�� exp

��ð1� aaÞFRT

ha

��(7)

jc ¼ j0;c

�exp

��acFRT

hc

�� exp

�ð1� acÞFRT

hc

��(8)

where j0 is exchange current density, a is transfer coefficient,

and h is overpotential defined as:

h ¼ E� E0 (9)

Electrode overpotential is defined here as the variation of

potential from the standard potential, rather than reversible

potential predicted by the Nernst equation, since the effect of

changing bulk concentrations was quite small compared to

the magnitude of standard potentials. Physicochemical pa-

rameters and constants are shown in Table 3. Overpotential is

a combination of purely kinetic activation and additional

concentration overpotentials that occur when reactant con-

centrations at CLs fall below reference values due to mass

transport limitations. The concentration dependency of ex-

change current density is adapted from Ref. [35]:

j0;a ¼ jref0;a

CCLGLY

CrefGLY

!gGLY CCLOH

CrefOH

!gOH

(10)

j0;c ¼ jref0;c

CCLO2

CrefO2

!gO2

(11)

where ðCCLi =Cref

i Þ is the ratio of species concentration at the

catalyst layer to the reference value, and g is reaction order,

assumed to be 1.0.

Table 3 e Physicochemical parameters and constants.

Parameter Symbol Value Units Reference

Anode standard

potential

E0a �0.77 V vs. SHE [25]

Cathode standard

potential

E0c 0.40 V vs. SHE [25]

Number of electrons

transferred

n 8.0 e [25]

Anode exchange

current density

j0;a 4.0 A m�2 Fitted

Cathode exchange

current density

j0;c 0.31 A m�2 Fitted

Anode transfer

coefficient

aa 0.42 e Fitted

Cathode transfer

coefficient

ac 0.58 e Fitted

DLC of anode CL Ceff;a 653 F m�2 EIS

DLC of cathode CL Ceff;c 653 F m�2 EIS

Universal gas

constant

R 8.314 J (mol K)�1 e

Faraday's constant F 96,485.3 C mol�1 e

Double-layer capacitanceEnergy is stored in or released from the reaction interface

when electrode potential changes, due to charging or dis-

charging of the electric double layer capacitance (DLC). The

current associated with the charging/discharging contributes

to cell current density (Icell), but not the faradaic currents

densities (ja, jc). As a result, DLC effectively smoothens the

faradaic current response to a change in conditions, and the

time response is dependent on the effective capacitance (Ceff)

of the electrode DLC:

Caeff

dha

dt¼ Icell �

��ja�� (12)

Cceff

dha

dt¼ Icell �

��jc�� (13)

where the left-hand side represents the DLC charging/dis-

charging current. At steady state the DLC behaves like an

open-circuit and relationship of cell and faradaic currents

simplifies to:

Icell ¼��ja�� ¼ ��jc�� (14)

Cell voltageCell voltage is calculated as:

Vcell ¼ E0cell � jhaj � jhcj � Icell

�Rcontact þ lm

sm

�(15)

where E0cell is the standard cell potential ðE0

c � E0aÞ, Rcontact is the

bulk contact resistance, and lm/sm is the membrane

resistance.

Numerical solution to AEM-DGFC modelsThe coupled system of mass transport, electrochemical ki-

netics, and cell voltage equations was solved using finite

element methods in a commercial software package, COMSOL

Multiphysics®. The boundary and initial conditions from Table

4 were applied. A linear interval was constructed to interpret

the 1-D geometry domain, and was divided into 100 elements

by applying a mesh grid. Each element was 0.003 mm, which

resulted in good solution resolution. Steady state polarization

tests were simulated using a parametric sweep of voltage or

current. Dynamic operation tests were simulated using a

second-order backward differentiation formula to discretize

time derivatives and a PARDISO direct linear solver to predict

the response to step changes in cell current density.

Experimental methods

Original laboratory experiments were performed on an AEM-

DGFC with Au/C anode catalyst to verify the mathematical

model and extract key modeling parameters. Detailed exper-

imental setup of the fuel cell and testing station and catalyst

synthesis details were given in previous publications and only

new methods are covered here [27,30].

AEM-DGFC setup and testing methodsFuel cell tests were performed on 850e Scribner fuel cell test

stand with a 5.0 cm2 fuel cell fixture (Fuel Cell Technologies).

The anode catalyst was self-prepared Au/C (55 wt% Au)

Table 4 e Initial and boundary conditions.

Condition Domain Parameter Value Units

Dirichlet boundary: x ¼ x0 Ci Crefi M

x ¼ x3 CO2 CrefO2

M

Neumann boundary: x ¼ x1 Ni

��ja��si=nF mol m�2 s�1

x ¼ x2 NO2

��jc��sO2=nF mol m�2 s�1

Initial conditions:

ðt ¼ 0Þx ¼ x0 / x1 Ci Cbulk

i M

CO2 0 M

x ¼ x2 / x3 Ci 0 M

CO2 CbulkO2

M

i ¼ GLY, TAR, or OH.

Fig. 2 e Equivalent circuit model diagram of AEM-DGFC

impedances from ohmic losses (R1), activation and

concentration overpotentials (R2), inductance (L), and

double layer capacitance (CPEdl).

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prepared by aqueous-phase reduction method, blended with

PTFE (5.0 wt% PTFE) and applied to a carbon-cloth liquid

diffusion layer. The cathode used non-noble metal catalyst

(FeeCu based 4020 catalyst, Acta), blended with AS-4 ionomer

(Tokuyama), and applied directly to an AEM (A-901 Tokuyama,

10 mm). Carbon paper (Toray) was used as the cathode gas

diffusion layer. Humidified high-purity O2 (>99.999%) or air

was fed into the cathode compartment at atmospheric back-

pressure and 0.4 L min�1. The cathode fuel and cell tempera-

ture were kept at 60 �C.Steady state polarization curves were collected by sweep-

ing current density from zero to the limiting condition by in-

crements of 20mA cm�2 and recording the cell voltage at each

point. Each point was held for 2 min to ensure a stable cell

voltage was recorded. The internal cell resistance (IR) was

simultaneously measured using the current-interrupt tech-

nique. Additionally, a Hg/HgO (1.0 M KOH) reference electrode

was inserted directly into the anode chamber and used to

monitor the anode potential. Cathode potential (Ec) was

calculated from the measured cell voltage, anode potential

(Ea), and internal resistance by:

Ec ¼ Vcell þ Ea þ IR (16)

Experimental anode and cathode potentials were con-

verted fromV vs.Hg/HgO (1.0 M KOH) to SHE by adding 0.098 V

[47]. Finally anode and cathode overpotentials at each current

density were calculated from the standard electrode poten-

tials with Equation (9).

The dynamic behavior of an AEM-DGFC was evaluated by

performing step changes of current density and monitoring

the cell voltage response over time. Current density step

changes from 100 to 150 to 100mA cm�2 were performed, with

the cell voltage allowed to stabilize at each condition. The

time to reach steady state was determined as the point where

the studied variable changed less than 0.1% per second.

Electrochemical impedance spectroscopy (EIS) to estimate DLCElectrochemical impedance spectroscopy (EIS), is a powerful

diagnostic tool used to measure the frequency dependency of

fuel cell impedance which uniquely capable to distinguish be-

tween the influences of different losses, such as membrane,

charge transfer, mass transfer, and double-layer capacitance

(DLC) [48]. Therefore, EIS was performed on an AEM-DGFC to

estimate the effective capacitance of the DLC, which is a key

parameter of the dynamic model. Two-electrode EIS tests were

conducted at eight DC current set points ranging from 50mA to

1.25 A. Frequency response analyzer (880 Impedance Analyzer,

Scribner-Associates) applied AC perturbations with 5% of DC

current amplitude to the load at frequencies sweeping from

10,000 to 0.1 Hz, and recorded the whole cell impedance

response. EIS results were analyzed by fitting the equivalent

circuit model shown in Fig. 2 to the measured impedance

spectra with commercial electrochemistry software ZView

(Scribner-Associates). Membrane and contact resistances

depend on external cell current and were modeled as a single

resistor (R1) with a value set equal to total ohmic resistance

previously measured by the current-interrupt method. Activa-

tion and concentration polarization are electrode phenomenon

anddependon faradaic current, and thereforemustbemodeled

in parallel with theDLC to account for the charging/discharging

current at the electrode surface. Combined activation and

concentration impedances were modeled as a resistor (R2) in

series with an inductor (L), to account for low-frequency

inductive effects, and in parallel to the DLC. A constant phase

element (CPE) was chosen to represent the DLC, in place of an

ideal capacitor. CPE is a theoretical circuit element that is

commonly used to model non-uniform capacitance along real

electrode-membrane interfaces [49]. The effective capacitance

of a CPE (Ceff) is estimated by:

Ceff ¼ Qo umaxð Þ4�1 (17)

where Qo is the CPE time constant, umax is the angular fre-

quency where maximum imaginary impedance occurs, and 4

is the exponent of phase angle [50].

Results and discussion:

Steady state modeling of AEM-DGFC

Steady state operation and model validationExperimental polarization and power density curves for AEM-

DGFC under the operating conditions in Table 4 are shown in

Fig. 3 e Experimental and predicted (a) polarization and power density curves and (b) absolute values of anode and cathode

overpotentials vs. current density. Conditions: 60 �C; anode: 1.0 M GLY þ 8.0 M OH; cathode: high purity O2.

Fig. 4 e Specific absolute values of overpotentials from

ohmic, anode (activation only and total), and cathode

losses vs. current density.

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Fig. 3(a), together with the simulated results from steady state

modeling for comparison. Important parameters of Butler-

eVolmer equation were determined by fitting the cur-

rentevoltage behavior, including exchange current densities

ðjref0 Þ and transfer coefficients (a) for GOR and ORR (Table 3).

However, fitting the model to cell voltage data alone cannot

distinguish the individual contribution of losses fromthe anode

and cathode reactions, so it was necessary to also consider the

experimental anode and cathode overpotentials. Anode and

cathode exchange current densities were found to be 4.0 Am�2

and 0.31 A m�2, respectively and predicted overpotentials are

shown vs. current density in Fig. 3(b), along with experimental

results. Although Fig. 3(b) matches experimental data fairly

well, the model does not predict the significant losses at OCV

seen experimentally,which is a limitation of this kineticmodel.

Specific voltage lossesFig. 4 shows the specific overpotentials from ohmic, anode,

and cathode losses vs. current density, simulated at condi-

tions in Table 5. The ohmic losses, from bulk contact and

membrane resistances, were found to be aminor contribution

to total loss in the AEM-DGFC, which is partially explained by

the high ionic conductivity and small thickness (10 mm) of the

AEM. Anode losses were a combination of GOR kinetic acti-

vation and liquid-phase reactant (GLY, OH) concentration

polarization. Cathode losses were almost entirely from ORR

activation, while O2 concentration polarization was negligible

in the gas-phase cathode DL. It was found that cathode acti-

vationwas the largest source of loss in the low current density

range, due to relatively slow ORR kinetics under these condi-

tions. Large ORR activation overpotentials are not surprising,

when considering the use of the non-noble metal cathode

catalyst and ambient pressure O2 supply. Yet, anode over-

potential became dominant in the middle current region, as

mass transport limitations in the anode liquid DL were

increased. The predicted results suggest that AEM-DGFC per-

formance depends on a delicate balance of GOR and ORR

activation losses with the anode concentration polarizations.

Effect of changing glycerol concentrationFig. 5(a) shows predicted cell voltage and power density vs.

current density for 0.50, 0.75, and 1.0 M bulk GLY

concentrations. It is clear that cell performance was drasti-

cally decreased at lower bulk glycerol concentrations. Both

peak power density and limiting current density were

decreased corresponding to a sharp increase in anode over-

potential at high current density, which is shown in Fig. 5(b),

along with local GLY concentration at the anode catalyst layer

(CL). It is well known thatmass transport often dominates fuel

cell performance in the high current density region. In the

case of AEM-DGFC, liquid-phase diffusion of fuel through the

porous anode DL was found to be a limiting factor due to the

relatively slow diffusion rate of glycerol in aqueous solutions

compared to other common fuels (DMethanol,water ¼3.7 � 10�9 m2 s�1, DGLY,water ¼ 2.8 � 10�9 m2 s�1 at 333.15 K

[45]). For instance, local glycerol concentration at the anode CL

reached nearly zero at a current density of only 150 mA cm�2

when 0.5 M GLYwas applied, and peak power density dropped

by 40% to 26.2 mW cm�2, compared to 43.9 mW cm�2 at 1.0 M

GLY concentration. Relatively high concentrations of GLY

alleviated the diffusion limitation due to the higher driving

force for mass transport and improved cell performance, and

Table 5 e Operation conditions and parameters.

Parameter Symbol Value Units Reference

Temperature T 333.15 K [30]

Cathode pressure P 1.0 atm [30]

Bulk concentration GLY CbulkGLY 1.0 M [30]

Bulk concentration OH CbulkOH 8.0 M [30]

Bulk concentration TAR CbulkTAR 0 M e

Bulk concentration

O2 (pure)

CbulkO2

P/RT M e

Bulk concentration

O2 (air)

e 0.21 P/RT M e

Reference GLY

concentration

CrefGLY 1.0 M [30]

Reference OH

concentration

CrefOH 8.0 M [30]

Reference oxygen

concentration

CrefO2

P/RT M [30]

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are therefore recommended for efficient and balanced AEM-

DGFC operation.

Effect of changing alkaline concentrationFig. 6(a) shows predicted cell voltage and power density vs.

current density for 2.0, 4.0, and 6.0, and 8.0 M bulk OH con-

centrations. As with the GLY study, cell performance was

decreased at lower OH concentration, however the effect was

not as severe in this case. Cell voltage dropped slightly with

decreasing bulk OH concentration from 8.0 to 4.0 M over the

current density range, however the limiting current density

was almost unchanged, only dropping from 295 to

283mA cm�2. However, when 2.0MOH bulkwas applied, local

OH concentration was low enough (~1.0 M) to significantly

limit the kinetics of GOR and resulted in additional concen-

tration overpotential and both limiting current and peak

power density were decreased. Fig. 6(b) reveals the relation-

ship of anode overpotential and local OH concentration at the

anode CL with changing bulk OH concentrations. It was found

that the local OH concentration at the anode CL remained

sufficiently high to facilitate GOR when at least 4.0 M OH was

used, and it can be deduced that mass transport of GLY, not

OH, was mainly limiting the cell performance. This demon-

strates that although OH diffusivity is greater than glycerol

Fig. 5 e Predicted (a) polarization (bold) and power density curv

concentration at anode CL (thin) for various GLY bulk concentra

(Table 2), mass transport limitations in the anode DL still may

occur if proper operating conditions are not met. It should be

noted that studies of other alkaline anion-exchange mem-

brane fuel cell systems observed a “volcano-type” relationship

of cell performance with base concentration, where

increasing alkaline concentration was beneficial to a point,

then had a negative effect above a tipping point concentration

[51e53]. A proposed explanation comes from the competitive

adsorption between OH and alcohol fuel, where too high base

concentrations may prevent adequate alcohol adsorption to

the active catalytic sites [54]. This phenomenon would not be

predicted by this model since a main assumption is that

reactant species availability is predominately diffusion

controlled. However, in the future this can be considered by

the addition of a surface reaction model that includes

adsorption/desorption steps coupled with electrochemical

surface reaction kinetics.

Effect of changing oxygen concentrationCathode gas purity and pressure are critical parameters that

determine the concentration of oxygen in the gas phase,

and therefore also effect the ORR kinetics. However, using

high purity and pressure O2 may not always be practical

solutions, due to added fuel costs. Fig. 7(a) and (b) show the

steady state predictions of cell voltage and cathode over-

potential, respectively, vs. current density using pure O2 or

air (21 mol% O2) at ambient pressure. The cathode fed with

air resulted in a decreased cell voltage of about 100 mV and

a peak power density drop of about 30% compared to that

with pure O2. The cell voltage drop was caused by the

decreased ORR kinetics and increased cathode over-

potentials resulting from lowered O2 bulk concentration.

However, compared to GLY diffusivity in the liquid phase

anode reaction/diffusion system, O2 delivery in the gas

phase is several magnitudes faster (Table 2) and additional

mass transport limitations did not occur at high current

densities. This was made evident by the limiting current

density only decreasing from 295 to 278 mA cm�2 when fed

with air and the flat cathode overpotential behavior at high

current densities. In other terms, operation with pure O2

achieves greater power density than air, but has little effect

on the losses at high current density, which have been

shown to be dominated by GLY diffusion in the anode DL.

es (thin) and (b) anode overpotential (bold) and GLY

tions.

Fig. 6 e Predicted (a) polarization (bold) and power density curves (thin) and (b) anode overpotential (bold) and OH

concentration at anode CL (thin) for various alkaline bulk concentrations.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 919774

Effect of changing anode DL porosityFig. 8(a) shows the predicted polarization and anode over-

potentials vs. current density for anode DL porosity values

ranging from 0.4 to 0.7. Cell performance was very sensitive to

reactant species delivery at the anode, and even a small

change in DL porosity resulted in significant difference in cell

voltage when current density was greater than 100 mA cm�2,

the region where mass transport losses becomes evident. The

decrease in cell voltage is attributed completely to the

increased anode overpotentials as the DL porosity, and

therefore effective diffusivities (Equation (5)) were decreased.

Fig. 8(b) gives the GLY concentration profile within the anode

DL at cell voltage of 0.1 V, where operation is close to the

limiting current density. The GLY concentration gradient with

respect to position became increasingly negative and the

steady state concentration at the anode CL (position¼ 0.3mm)

varied from 188 to 50 mM as porosity decreased. The steady

state parameter analysis of anode DL porosity demonstrated

the high sensitivity of GOR to electrode design and mass

transport resistances.

Dynamic modeling of AEM-DGFC

Dynamic operation and model verificationThe time-dependent model was verified by comparison with

experimental results of an AEM-DGFC operated with up/down

Fig. 7 e Predicted (a) polarization (bold) and power density (thin

operation with high purity O2 or air.

step changes in current density. At the first step change,

current density increased from 100 to 150 mA cm�2 and the

model accurately predicted a rapid drop in cell voltage fol-

lowed by gradual leveling, as shown in Fig. 9(a). Cell voltage

stabilized to the value predicted by the steady state model,

with little error compared to the experimental result. At the

second step change, current density decreased from 150 to

100 mA cm�2 and cell voltage responded with a rapid increase

before gradually returning to the steady state voltage. Due to

the good agreement of the simulated and experimental re-

sults, we conclude that the model is a reasonable represen-

tation of the real dynamic mechanisms. Furthermore, the

specific contributions of ohmic, activation, and concentration

overpotentials to the dynamic cell voltage response were

predicted and shown in Fig. 9(b). The change in ohmic loss

includes ionic transport resistance in the AEM and bulk con-

tact resistances, which are non-electrode processes and

change instantaneously with current density in this model, as

demonstrated by a vertical line at the time of step change.

Kinetic activation is dependent on faradaic current, which

does not vary instantaneously with cell current density due to

DLC effects. However, it was found that activation over-

potential reached the new steady state value very quickly, in

less than 1 s. In contrast the concentration losses, which are

also dependent on the DLC charging/discharging process,

required much longer relaxation times to reach steady state

) curves and (b) absolute values of cathode overpotential for

Fig. 8 e Predicted (a) polarization (bold) and anode overpotential (thin) curves and (b) GLY concentration profile through

anode DL at cell voltage ¼ 0.1 V for different anode DL porosities.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 9 19775

due to time-dependent species mass transport. Therefore, it

can be concluded that the DLC effect is negligible in the AEM-

DGFC when compared to the much slow diffusion processes

which determine the dynamic behavior.

Identifying contributions of dynamic mechanisms withchanging load conditionsFuel cell dynamic response is controlled by complex physi-

cochemical phenomena involving a wide range of time scales.

Fig. 10(a) shows predicted overpotential split into the anodic

and cathodic components for current density step changes of

100e150e100mA cm�2, in order to identify their contributions

to the transient cell voltage response time. As seen in

Fig. 10(a), and summarized in Table 6, cathode overpotential

reached steady state about three magnitudes faster than

anode overpotential. Even though anode and cathode over-

potentials were both significant contributions to the steady

state voltage loss under these conditions, the model predicts

that the transient voltage behavior is mainly from the anode.

This can be attributed to the far slower diffusion rates of GLY

and OH in the liquid-phase anode DL compared to O2 inside

the gas-phase cathode DL. In order to more closely evaluate

Fig. 9 e (a) Experimental and predicted dynamic response of ce

100e150e100 mA cm¡2 and (b) specific contributions of ohmic,

response to 100e150 mA cm¡2 step change.

the transient anode losses, Fig. 10(b) shows predicted local

anode species (GLY, OH) concentration and corresponding

overpotentials over time in response to 100e150e100

mA cm�2 step changes. Fig. 10(b) shows that local GLY con-

centration at anode CL and GLY concentration overpotential

reached steady state in a similarway over 132e140 s, while OH

concentration reached steady state after only 73 s. The rela-

tively slow anode dynamics are therefore attributed specif-

ically to the non-steady state diffusion of GLY in the anode DL,

based on the evidence that GLY stabilization occurred over the

same approximate time scale as anode potential, and the fact

that GLY concentration overpotential was about ten times

greater contribution than that of OH.

Surprisingly, longer durations were needed for over-

potentials and cell voltage to reach steady state for steps of

increasing current density (step 1) than for decreasing current

density (step 2). However, the time to reach steady state GLY

concentration, which was the major contribution to transient

behavior, did not depend on step direction. The explanation

for this phenomenon comes from the governing equations of

GLY mass transport and anode concentration overpotential.

The first-order kinetics governing concentration loss gives

ll voltage to up/down step changes in current density of

activation, and concentration overpotentials to dynamic

Fig. 10 e Predicted dynamic response of (a) absolute values of anode and cathode overpotentials and (b) GLY and OH

concentrations at anode CL and concentration overpotentials to step changes of 100e150e100 mA cm¡2.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 919776

that overpotential is proportional to natural log of local GLY

concentration, and therefore a derived relation for the rate of

change of anode concentration overpotential is given by:

vha;GLY

vtf

�1

CGLY

vCGLY

vt

�(18)

where the rate of change of anode concentration over-

potential from GLY is not only directly proportional to the rate

of change of local GLY concentration but also inversely pro-

portional to local GLY concentration. In effect, anode over-

potential will reach a steady state value faster when GLY

concentration is low, which corresponds to high current

densities.

Effect of changing anode DL porosity on dynamic responseThe dynamic cell behavior was strongly dependent on the

transient mass transport of GLY and OH in the anode DL, and

it may be desirable to alter the DL design to improve the

response to changing conditions. Dynamic simulations were

performed to explore the effects of anode DL porosity on the

local GLY concentration response to 100e150e100 mA cm�2

step changes and results are summarized in Fig. 11 and Table

7. It is demonstrated that GLY concentration response time

was very sensitive to anode DL porosity, reaching steady state

faster with increasing porosity. While the anode DL must

provide a solid, electrically conductive pathway for electron

collection, it must also be sufficiently porous to allow efficient

delivery and removal of reaction species. An anode DL with

low porosity may be preferred to reduce electron transport

Table 6 e Dynamic responses of study parameters to100e150e100 mA cm¡2 step changes.

Study parameter Step 1 (s) Step 2 (s)

Cell voltage 100 91

Anode overpotential 112 104

Cathode overpotential 0.2 0.2

GLY concentration at CL 136 136

GLY concentration overpotential 140 132

OH concentration at CL 73 73

OH concentration overpotential 74 73

resistance, however the effective diffusion rates of reaction

species will suffer.

Estimating dynamic parameters with electrochemicalimpedance spectroscopy (EIS)

EIS spectra at DC current set points from 50 mA to 1.25 A are

shown in Fig. 12. The observed Nyquist plots have the shape of

a depressed semi-circle loop in the negative ZIm region and a

smaller loop in positive ZIm that becomes more developed

with higher current densities, associated with low-frequency

inductive effects. The inductance loop observed in fuel cell

EIS has been previously attributed to the relaxation of adsor-

bed intermediate species during multi-step electrode re-

actions [55]. Electrocatalytic oxidation of GLY on Au/C catalyst

is a complex reaction involving adsorbed intermediates spe-

cies [30], which could explain the observed inductance effect.

However it is beyond the scope of this study to identify the

specific contributions of the anode or cathode reactions.

Fig. 11 e Predicted dynamic response of GLY concentration

to step changes in current density of

100e150e100 mA cm¡2 at different anode DL porosities.

Table 7 e Effect of changing anode DL porosity ondynamic response of GLY concentration to100e150e100 mA cm¡2 step changes.

Porosity Steps 1 (s) Step 2 (s)

ε ¼ 0.40 225 225

ε ¼ 0.50 161 161

ε ¼ 0.56 136 136

ε ¼ 0.60 123 123

ε ¼ 0.70 98 98

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 9 19777

The equivalent circuit model shown in Fig. 2 was fitted to

the experimental impedance data by finding the optimized

values of R2, L, Qo, and 4 at each DC current, summarized in

Supplementary Content, Table S1, along with a comparison of

experimental cell resistance between EIS and steady state

polarization tests. Note, a constant value of ohmic resistance

(R1) was assigned, as measured by the current-interrupt

method. The ‘goodness’ of the equivalent circuit model fit

was quantified by the weighted sum of squared error, which

ranged from 0.346 to 2.87 � 10�2. The greatest error was found

for the lowest current, 0.05 A, at which point the observed

inductance effect was diminished, which introduced error in

the inductor circuit element.

In this method, EIS measures the combined impedances of

anode and cathode, however the specific contributions of each

electrode are not distinguishable from the single negative ZIm

loop observed. This is explained by one of two cases. First, the

EIS spectra could be attributed to a single half-cell reaction if

the other reaction occurs with negligible activation polariza-

tion, as is the case for H2/O2 PEM fuel cells where the hydrogen

oxidation reaction at the anode is much more facile than ORR

at the cathode [56e58]. Second, if the two half-cell time con-

stants are comparable magnitudes then the two semi-circles

merge and a single semi-circle is formed that corresponds to

the total cell impedance [57]. We propose the second case for

AEM-DGFC, since liquid-phase GOR occurs much slower than

HOR, and was shown to have activation losses on the same

Fig. 12 e Nyquist plots of cell impedance from EIS tests at

0.05 Ae1.25 A.

magnitude as ORR (see Fig. 3(B)). Effective capacitance was

calculated for each cell current from the fitted CPE parameters

(Qo and 4) and the frequency where maximum �ZIm occurred.

The calculated values fluctuated near a mean value of

326 F m�2, ranging from 261 to 366 F m�2, based on geometric

reactor area. Under the hypothesis that the anode and cath-

ode impedances occur over the same time scale, it is reason-

able to assume the half-cell effective capacitances are

approximately equal. As a result, the half-cell capacitances

are equal to two times the total capacitance, or 653 F m�2, as

calculated by the inverse rule of capacitances in series. To the

best of our knowledge, no such parameter has been previously

reported for an AEM-DGFC, however this value does fall

within the range of 100e1000 F m�2, previously reported in a

classic DMFC impedance study [55].

Recall that the dynamic response time of the DLC charging/

discharging was found to be negligible compared to the slow

diffusional processes. In fact, increasing the capacitance pa-

rameters by ten times resulted in the time to reach steady

state cell voltage increasing by only ~1%, for a

100e150 mA cm�2 current density step. So, although the

equivalent circuit method of estimating the effective capaci-

tance relies some on averaging and estimation, the values are

confidently within the correct magnitude of the true capaci-

tance, and therefore are suitable for use in the dynamic AEM-

DGFC model.

Conclusions

A simple, single-product kinetic model with one-dimensional

species transport was developed which accurately predicted

the steady state voltage losses and dynamic response to

changing load conditions in an AEM-DGFC. Significant ORR

activation overpotentials at the cathode contributed to losses

in the low current density region, while anode overpotential

was the major source of loss at middle to high current den-

sities, due to limited glycerol diffusion in the catalyst layer.

The effect of changing fuel concentration was investigated

and it was found that performance was very sensitive to GLY

bulk concentration, but high alkaline concentrations allevi-

ated significant OH mass transport losses. Prediction of dy-

namic response of AEM-DGFC, including time-dependent

species transport andDLC charging, to step changes in current

density revealed that liquid-phase reactant diffusion was a

key factor influencing the transient AEM-DGFC behavior and

was very sensitive to diffusion layer design. In comparison,

mass transport losses at the cathode were negligible due to

fast O2 transport in the gas-phase diffusion layer. As a result,

the dynamic response of cathode overpotential was controlled

by ORR activation losses and reached steady state quickly and

therefore did not contribute to the overall cell response time.

EIS with equivalent circuit modeling allowed parameter esti-

mation of anode and cathode effective capacitances and

further supported the dynamic model.

This work demonstrates a new mathematical model for

AEM-DGFC, which accurately predicted cell performance and

behavior undermany simplifying assumptions. Future studies

will build upon this work by incorporating: (1) multiple

oxidation products and varying product selectivity, (2)

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 9 7 6 7e1 9 7 7 919778

detailed reaction sequence of adsorption/desorption and

surface reactions, (3) non-isothermal conditions with Arrhe-

nius temperature-dependent rate law, and (4) species mass

transport by convective flow. These additional complexities

allow for more traditional kinetic analysis and form an even

better representation of the physicochemical processes and

selective oxidation in AEM-based alcohol fuel cells. The

development of robust, validated theoretical simulations in

parallel with advanced experimental techniques is critical for

future breakthroughs in electrocatalytic production of chem-

icals and energy from biorenewables.

Acknowledgments

This work is partially supported by the U.S. National Science

Foundation (CBET-1159448) and Michigan Tech REF-RS

(E49290). J. Qi is grateful to financial support from the Chinese

Scholarship Council.

Nomenclature

AEM anion-exchange membrane

AEM-DGFC anion-exchange membrane e direct glycerol fuel

cell

CL catalyst layer

CPE constant phase element

D diffusion coefficient

DL diffusion layer

E potential

F Faraday's constant

GOR glycerol oxidation reaction

Icell cell current density

j0 exchange current density

ORR oxygen reduction reaction

n number of electrons transferred per molecule

N molar flux

Qo first CPE coefficient

s stoichiometric coefficient

V voltage

Greek

a transfer coefficient

ε diffusion layer porosity

h overpotential

s conductivity

u angular frequency

4 second CPE coefficient

Sub/superscripts

a anode

c cathode

GLY glycerol

i chemical species

O2 oxygen

OH hydroxide ion

TA tartronic acid

TAR tartronate ion

Appendix A. Supplementary data

Supplementary data related to this article can be found at

http://dx.doi.org/10.1016/j.ijhydene.2014.08.144.

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